Question

Let N be the least positive integer such that whenever a non-zero digit c is written after the last digit of N, the resulting number is divisible by c. Then the sum of the digits of N is:-

(a) 9

(b) 18

(c) 27

(d) 36

Answer 1

The correct option is (a) 9.

N is least positive integer and when a digit c is written after last digit of N, the resulting number is divisible by c.

⇒  So, (N)c / c​

Least positive integer (N) which is divisible by digit c i.e. (1−9)

So possible number is

⇒ (9 × 8 × 7 × 5)c​ / c

Number, 9 × 8 × 7 × 5 is divisible by all the digits from 1 to 9

⇒  So, Number is 72 × 35 = 2520 = N

⇒  Sum of the digits of number N = 2 + 5 + 2 + 0 = 9